The biggest difference in Barzal's production under Weight vs. this season was his powerplay production and not having Tavares to run the PP for him. Even under Trotz' defensive system, Barzal put up 5v5 points at an elite level -- only 7 players had more 5v5 points than him and of those 7, only McDavid, Mathews and Marner outproduced him by 5 points or more. Heck, he even had more 5v5 points than MacKinnon. He was on pace to put up ~95% of the 5v5 points he put up under Weight over the same number of games, whereas he was on pace for ~44% of the PP pts. And while we can fault the powerplay system to a certain extent for his lack of overall production, Leddy, Nelson, Wahlstrom and Bailey all outproduced him in PP pts this season and Pageau tied him, which should not happen given that he had notably more PP TOI than each of them and how much of the PP he spends with the puck on his stick.
If he wants to be an elite offensive player in the league, he needs to improve his play on the PP. Too often we watch him hold the puck for lengthy periods of time while the PKers are happy to let him stand there looking for the perfect pass and eat up time, as they know he isn't going to shoot. He needs to move the puck quicker, move his feet more to draw PKers out of position and shoot more. I'm not trying to say he wouldn't benefit from a higher level of talent around him, but a lot of it is on him too.